Investigation of continuous time Markov chain approximate transient analysis via subgraph generation in the case of a car sharing system model

Abstract

We present an investigation of the generation of partially absorbing continuous time Markov chains (CTMCs) for the purpose of approximating transient analysis of the underlying Markov chain. The Markov chain model of a car-sharing system, considering realistic parameter values such as fleet size and number of zones, is too large to be analyzed in its entirety. To obtain an approximate estimation of the changes in system characteristics starting from a given initial state, it is sufficient to generate and analyze a small fraction of the complete CTMC. We address the problem of identifying which states should be included for analysis by employing subgraph generation algorithms. The numerical results validate some of our insights about the problem and also provide suggestions for further research.